Mechanical Analysis On The Spherical Cavity Expansion Problem In Geomaterials

Geomaterials, which belong to typical pressure sensitive materials, are the most widely used materials in the nature. As they contain micro-structures (such as micro-voids, defects and cracks), the deformation and failure mechanism are complicated. Their mechanical properties are significantly different from those of metal materials, which mainly being shown in non-linear stress-strain relations, apparent hardening or softening characteristics, and hydrostatic pressure's effectiveness to their yield, injury and failure. Because having the similarity of micro-meso structure, study on the constitutive equations of geomaterials has important reference value for study of cement, concrete, reinforced concrete, and some other new materials such as foam metals.As the spherical cavity expansion model has the property of being symmetry, simple, and clear, it can provide the solution of stress and strain field easily so as to reveal the nature of materials'deformation, therefore it is widely used in fields of solid mechanics, materials science, solid state physics and explosion mechanics, etc. In this paper, problems of spherical cavity expansion in geomaterials had been studied by using a four-region model, changes of stress and displacement in plastic, damage and elastic regions were discussed under conditions of static and dynamic expansion. Because using the idea of dividing the model into different regions with different distortion mechanism, different constitutive equations were adopted. The main work of this paper is as follows:1. Take a four regions' spherical cavity expansion model (plastic region/damage region/elastic region/stress-free region) as a research object, a damage region is thought being existed between plastic region and elastic region. As damage region connects constraints of both plastic region and elastic region, which means it is impossible to achieve complete destruction, we established a four-region spherical cavity expansion model withσθ≠0.2. Base on the theory of macroscopic plasticity and the continuous character of geomaterials'deformation, elliptical yield criterion are adopted, a increment type constitutive and a full-bore type equation are constructed to reflect materials'pressure sensitivity. And base on the theory of microscopic plasticity, a plastic yield criterion which reflects the effect of micro-structures to geomaterials' yield is deduced. A damage constitutive equation with Lemaitre effective stress is established also.3. Using the dividing idea mentioned above, plasticity and damage mechanics are adopted to analyze problems of static spherical cavity expansion in geomaterials, boundary conditions and continuity conditions at the junctions are given, changes of stress and displacement field and relationships between these field quantities and the material parameters are discussed in all the regions of plastic, damage and elastic. These provide a reference to gain a deeper understanding of the deformation nature of geomaterials.4. Via self-similar assumptions, elastic and damage mechanics are adopted to analyze problems of dynamic spherical cavity expansion in geomaterials by combining the three-region (damage zone, elastic zone and stress-free zone) model. Quantity distributions in damage zone and elastic zone are solved by shooting method with a single parameter, and impact factors of damage zone are discussed, from which it is pointed out that the material might be damaged under certain conditions, when a four-region model should be more reasonable to study the problem.5. Using elliptic yield criterion of pressure sensitive materials and the self-similar assumption, the plastic zone out of damage zone are adopted to analyze the field solution under conditions of the study in damage zone. Nonlinear differential equations of plastic region of the dynamic expansion are derived for both increment type (elastic-perfectly plastic materials) and full-bore type constitutive equation (power-hardening materials). Via three-zone model we discussed before to determine the plastic boundary conditions, numerical simulation are obtained by shooting method with two parameters, and the impact of material parameters are also discussed.Overall, the explosive fields of geomaterials are studied comprehensively by using four-region model of the spherical cavity expansion, researches on stress and displacement fields in plastic, damage and elastic zone will provide a deeper understanding of the geomaterials' deformation, meanwhile lay a deep foundation for theoretical research and subsequent engineering applications.